It is very possible this is the case. Especially since Menphina isn't a moon anymore then Dalamud was. Menphina, ironically given what she is a goddess of, is Zodiark's prison. So you've got two celestial bodies that are prisons for something with lots of aetheric power rotating around Hydaelyn. I am rather suspicious that the Allgans somehow figured out what Menphina really is and wondered if they could copy it.
Bahamut and the Waring Triad were probably locked up in Omega's force fields like Shinryu was. I can see the Allagans building the neurolinks/Dalamud around them before rupturing Omega's fields.
One theory (that I can see being true) is the the Dawn Throne is the remains of Dalamud's launch site or construction site. Given how off any sense of scale is in video-games, the Dawn Throne could easily be as big as Dalamud was. One of the biggest hurdles to overcome to get an object into orbit is weight and Dalamud would have been very, very heavy. So it would need a lot of power to get into orbit. The Dawn Throne isn't that from from the House of the Crooked Coin, so I can see the Allagans watching the launch happen over on the Dawn Throne while they control it from the House. And both the Dawn Throne, the stone pillars around it, and the Crystal in the House have identical motifs carved/drawn on them.
Given how Allagan artifacts don't age, I can see the Dalamud launch/construction site filling with debris over five millennia until the Oronir eventually settled on top of it. It's far enough away from the Crystal Tower for the 4th Umbral Calamity to not have sunk it like the Allagan Capital and Crystal Tower were. For all that the Xaela don't have modern mechanical technology, their skill in enchanting golems like Bardam and carving semi-autonomous chuluu seems to indicate that they do have an advanced knowledge of how aether can be used to effect their surroundings. I can see that being a surviving remnant of the Allagans' knowledge of aetherochemistry, as that part of it wouldn't rely on Allagan tech to function correctly.